Design of tangent vector fields
ACM SIGGRAPH 2007 papers
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Proceedings of the twenty-fourth annual symposium on Computational geometry
Resolving Loads with Positive Interior Stresses
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Gabriel meshes and Delaunay edge flips
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
A volume-based heat-diffusion classifier
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A spectral characterization of the Delaunay triangulation
Computer Aided Geometric Design
Growing self-reconstruction maps
IEEE Transactions on Neural Networks
Geodesic delaunay triangulations in bounded planar domains
ACM Transactions on Algorithms (TALG)
International Journal of Computer Vision
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Discrete Laplacians on general polygonal meshes
ACM SIGGRAPH 2011 papers
3D CAD model retrieval with perturbed Laplacian spectra
Computers in Industry
Robust modeling of constant mean curvature surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh
Computer Graphics Forum
Consistent approximations of several geometric differential operators and their convergence
Applied Numerical Mathematics
Extremum problems for eigenvalues of discrete Laplace operators
Computer Aided Geometric Design
SMI 2013: Laplacians on flat line bundles over 3-manifolds
Computers and Graphics
| Hi-index | 0.02 |
We define a discrete Laplace–Beltrami operator for simplicial surfaces (Definition 16). It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called “cotan formula”) except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace–Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa’s Theorem we show that, as claimed, Musin’s harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.